On computing the distribution function for the Poisson binomial distribution

Computational Statistics and Data Analysis

Volumn 59, Issue 1, 2013, Pages 41-51

  Hong, Yili ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Characteristic function; k out of n system; Longevity risk; Normal approximation; Sum of independent random indicators; Warranty returns

Indexed keywords

APPROXIMATION METHODS; BERNOULLI DISTRIBUTIONS; BINOMIAL DISTRIBUTION; CHARACTERISTIC FUNCTIONS; CLOSED-FORM EXPRESSION; CUMULATIVE DISTRIBUTION FUNCTION; EXACT FORMULAS; K-OUT-OF-N SYSTEM; NORMAL APPROXIMATION; POISSON APPROXIMATIONS; RECURSIVE FORMULAE; WARRANTY RETURNS;

APPROXIMATION ALGORITHMS; APPROXIMATION THEORY; DISCRETE FOURIER TRANSFORMS; NUMERICAL METHODS;

POISSON DISTRIBUTION;

EID: 84870066105     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2012.10.006     Document Type: Article

References (21)

1. K.B. Athreya, and S.N. Lahiri Measure Theory and Probability Theory 2006 Springer New York
2. R.E. Barlow, and K.D. Heidtmann Computing k-out-of-n system reliability IEEE Transactions on Reliability 33 1984 322 323
3. A. Bossavy, R. Girard, and G. Kariniotakis Forecasting ramps of wind power production with numerical weather prediction ensembles Wind Energy 2012 10.1002/we.526
4. R. Bracewell The Fourier Transform & its Applications third ed. 2000 McGraw-Hill, Inc. Singapore
5. X.-H. Chen, A.P. Dempster, and J.S. Liu Weighted finite population sampling to maximize entropy Biometrika 81 1994 457 469
6. S.X. Chen, and J.S. Liu Statistical applications of the Poisson-binomial and conditional Bernoulli distributions Statistica Sinica 7 1997 875 892
7. J.W. Cooley, and J.W. Tukey An algorithm for the machine calculation of complex Fourier series Mathematics of Computation 19 1965 297 301
8. D. Duffie, L. Saita, and K. Wang Multi-period corporate default prediction with stochastic covariates Journal of Financial Economics 83 2007 635 665
9. M. Fernández, and S. Williams Closed-form expression for the Poisson-binomial probability density function IEEE Transactions on Aerospace and Electronic Systems 46 2010 803 817
10. Y. Hong, and W.Q. Meeker Field-failure and warranty prediction based on auxiliary use-rate information Technometrics 52 2010 148 159
11. Y. Hong, W.Q. Meeker, and J.D. McCalley Prediction of remaining life of power transformers based on left truncated and right censored lifetime data The Annals of Applied Statistics 3 2009 857 879
12. W. Kuo, and M. Zuo Optimal Reliability Modeling: Principles and Applications 2003 John Wiley & Sons, Inc. Hoboken, NJ
13. L. Le Cam An approximation theorem for the Poisson binomial distribution Pacific Journal of Mathematics 10 1960 1181 1197
14. A. Niida, S. Imoto, T. Shimamura, and S. Miyano Statistical model-based testing to evaluate the recurrence of genomic aberrations Bioinformatics 28 2012 i115 i120
15. Pitacco, E.; 2007. Mortality and longevity: a risk management perspective. In: IAA Life Colloquium, Stockholm. Available at: http://www.actuaries.org/LIFE/Events/Stockholm/Pitacco.pdf.
16. R The R Project for Statistical Computing 2012 http://www.r-project.org/
17. S.M. Samuels On the number of successes in independent trials The Annals of Mathematical Statistics 36 1965 1272 1278
18. R.C. Singleton An algorithm for computing the mixed radix fast Fourier transform IEEE Transactions on Audio and Electroacoustics AU-17 1969 93 103
19. Tang, P.; Peterson, E.A.; 2011. Mining probabilistic frequent closed itemsets in uncertain databases. In: Proceedings of the 49th ACM Southeast Conference, ACMSE, Kennesaw, GA, pp. 86-91.
20. A.Y. Volkova A refinement of the central limit theorem for sums of independent random indicators Theory of Probability and its Applications 40 1996 791 794
21. Y.H. Wang On the number of successes in independent trials Statistica Sinica 3 1993 295 312